When I copied pages from one InDesign document to another by drop and drag, line breaks changed. All of the settings appear to be the same: text size and leading, tracking, kerning, hyphenation, paragraph composer, text frame size, margins. It seems like there must be some underlying setting that is different in the two documents. Any suggestions for where to look would be much appreciated.

First check whether the difference is real: go to the document you copied from and recompose it (type any character in the story and delete it). If the text doesn't change then there is indeed a difference, though I have nothing to offer. . .

Also, there could be an Object Style conflict—the two document's [Basic Text frame] styles could be different. When there is a conflict with same named styles the destination style definition is used.

Do you still have the problem if you break the style links? Select the text and choose Break Link to Style from the Paragraph Styles panel and do the same for the selected text frame in the Object Style panel and see if that fixes the problem.